<title>Optimal regularization parameter estimation for image restoration</title>

Abstract

Image restoration results that are both objectively and subjectively superior can be obtained by allowing the regularization to be spatially variant. Space-variant regularization can be accomplished through iterative restoration techniques. The optimal choice of the regularization parameter is usually unknown a priori. The generalized cross-validation (GCV) criterion has proven to perform well as an estimator of this parameter in a space-invariant setting. However, the GCV criterion is prohibitive to compute for space-variant regularization. In this work, we introduce an estimator of the GCV criterion that can be used to estimate the optimal regularization parameter. The estimator of the GCV measure can be evaluated with a computational effort on the same order as that required to restore the image. Results are presented which show that this estimate works well for space-variant regularization.